The overall aim of this proposal is the development, implementation, testing and evaluation of computer methods for image reconstruction in tomographic radiology, and the application and evaluation of the resulting software for some specific problems in medicine. Algorithms for image reconstruction from projections form the foundations of modem methods of tomographic imaging in radiology, such as computed tomography (CT) and positron emission tomography (PET). We aim at demonstrable improvements in the efficacy of reconstruction algorithms for specific applications of such radiological modalities. The proposed work is sub-divided into three symbiotic projects: (i) image modeling; (ii) image reconstruction algorithms; (iii) image evaluation. The first project aims at the development of a methodology to provide statistical models of ensembles of images so that random samples from these ensembles will resemble images that we are likely to come across in some specific radiological applications. The second project aims at improving the state of the art in the area of reconstruction algorithms, specifically by making use of the image models of the first project and considering the needs of the third project. The third project aims at developing and applying a methodology for the evaluation of the problem-specific efficacy of reconstruction algorithms. It will feed back to the first two projects by providing a means of problem-specific optimal selection of free parameters in both image models and in reconstruction algorithms. The combined result of the successful completion of these three projects will be the statistically rigorous demonstration of the superior medical efficacy of images produced by computationally efficient reconstruction algorithms which make use of image modeling priors. The health-related significance of this work is two-fold. In the short- term, it will lead to higher quality images in a number of clinically useful applications of CT and PET (in particular, in CT imaging of the lungs and PET imaging of the brain, the heart and the lungs). In the long- term, it will provide a theoretical foundation on which future major developments in the reconstruction aspects of medical imaging can be based and evaluated.